import numpy as np import matplotlib.pyplot as plt from itertools import permutations import math import openjij as oj import random # ============================ # 1. KDE 函數 # ============================ def kde_1d(samples, num_points=200): if len(samples) == 0: return np.array([]), np.array([]) xs = np.linspace(min(samples), max(samples), num_points) n = len(samples) if n < 2: return xs, np.zeros_like(xs) std = np.std(samples) if std == 0: std = 1.0 h = 1.06 * std * (n ** (-1/5)) ys = [] inv_sqrt_2pi = 1.0 / math.sqrt(2 * math.pi) for x in xs: s = 0.0 for xi in samples: z = (x - xi) / h s += math.exp(-0.5 * z * z) * inv_sqrt_2pi ys.append(s / (n * h)) return xs, np.array(ys) # ============================ # 2. route diversity matrix（支援可變長度路徑） # ============================ def route_diversity_matrix(routes, N): """ routes: list of routes，每條 route 是城市序列，例如 [0, 2, 5, 1, 9] 我們只用前 N 個位置來統計（超過 N 的部分忽略） """ freq = np.zeros((N, N), dtype=float) valid_routes = 0 for route in routes: if len(route) == 0: continue valid_routes += 1 for t in range(min(len(route), N)): city = route[t] if 0 <= city < N: freq[city, t] += 1 if valid_routes > 0: freq /= valid_routes return freq # ============================ # 3. MTSP 變數編碼：x[k,i,p] → index # ============================ def idx_mtsp(k, i, p, N): """ x[k,i,p] → 1D index """ return k * (N * N) + i * N + p # ============================ # 4. 建立 2-UAV M-TSP QUBO（城市數不固定） # ============================ def build_mtsp_qubo_variable(D, penalty=20.0, big_penalty=9999.0): """ - 城市: 0..N-1，其中 0 為 depot - 兩台 UAV: k = 0,1 - 每台 UAV 有 N 個 slot: p = 0..N-1 - 變數: x_{k,i,p} QUBO包含： 距離成本 + 位置約束 + 城市約束 + 起點約束 """ D = np.asarray(D) N = D.shape[0] Q = {} def addQ(u, v, w): if w == 0: return if u > v: u, v = v, u Q[(u, v)] = Q.get((u, v), 0.0) + w # ---- 距離成本 ---- for k in range(2): for p in range(N): q = (p + 1) % N for i in range(N): for j in range(N): dij = D[i, j] if dij == 0: continue u = idx_mtsp(k, i, p, N) v = idx_mtsp(k, j, q, N) addQ(u, v, dij) # ---- 位置約束：每 slot 只能一個城市 ---- for k in range(2): for p in range(N): vars_pos = [idx_mtsp(k, i, p, N) for i in range(N)] for u in vars_pos: addQ(u, u, -penalty) for a in range(N): for b in range(a+1, N): addQ(vars_pos[a], vars_pos[b], 2*penalty) # ---- 城市約束：1..N-1 每城恰好一次 ---- for i in range(1, N): vars_city = [] for k in range(2): for p in range(N): vars_city.append(idx_mtsp(k, i, p, N)) for u in vars_city: addQ(u, u, -penalty) L = len(vars_city) for a in range(L): for b in range(a+1, L): addQ(vars_city[a], vars_city[b], 2*penalty) # ---- 起點約束：每台 UAV 的 p=0 必須是 city 0 ---- for k in range(2): for i in range(1, N): addQ(idx_mtsp(k, i, 0, N), idx_mtsp(k, i, 0, N), big_penalty) addQ(idx_mtsp(k, 0, 0, N), idx_mtsp(k, 0, 0, N), -big_penalty) return Q, N # ============================ # 5. 解碼 slot 序列（不修剪） # ============================ def decode_slots(sample, N): """ 回傳： u1_slots, u2_slots 各自長度 N，裡面是城市 index（可能重複，也可能很多 0） """ slots = [] for k in range(2): row = [] for p in range(N): chosen = 0 # 預設當作待在 depot for i in range(N): if sample.get(idx_mtsp(k, i, p, N), 0) == 1: chosen = i break row.append(chosen) slots.append(row) return slots[0], slots[1] # ============================ # 6. 根據 slots 做 repair → 產生合法 uav1 / uav2 path # ============================ def repair_routes_from_slots(u1_slots, u2_slots, N): """ 依據 slots 傾向資訊，把城市分配給兩台 UAV， 並用暴力 TSP 在各自子集合裡找最短路徑，確保： - 每個城市 1..N-1 被恰好一台 UAV 拜訪 - 兩台 UAV 路徑皆為 0 -> ... -> 0（成本計算時處理） """ # 統計每個城市在兩台 UAV slots 中出現次數 count1 = [0]*N count2 = [0]*N for c in u1_slots: if 0 <= c < N: count1[c] += 1 for c in u2_slots: if 0 <= c < N: count2[c] += 1 # 分配城市：看誰出現次數多，平手則讓城市較少的一邊拿 assign1 = [] assign2 = [] for city in range(1, N): # city 0 = depot 不分配 if count1[city] > count2[city]: assign1.append(city) elif count2[city] > count1[city]: assign2.append(city) else: # 平手 → 給目前負載較少的 UAV if len(assign1) <= len(assign2): assign1.append(city) else: assign2.append(city) return sorted(assign1), sorted(assign2) # ============================ # 7. 單 UAV 成本 & 子集合最佳排列 # ============================ def uav_cost(path, D): if not path: return 0.0 path = [c for c in path if 0 <= c < len(D)] if len(path) == 0: return 0.0 cost = D[0, path[0]] for i in range(len(path)-1): cost += D[path[i], path[i+1]] cost += D[path[-1], 0] return float(cost) def best_order_for_cities(cities, D): """ 對給定 city set，暴力搜尋最短 0 -> perm -> 0 的路徑 cities: list of city index (1..N-1) """ if len(cities) <= 1: return list(cities), uav_cost(list(cities), D) best_perm = None best_cost = float('inf') for perm in permutations(cities): c = uav_cost(list(perm), D) if c < best_cost: best_cost = c best_perm = list(perm) return best_perm, best_cost # ============================ # 8. 利用 QUBO 取樣 + repair 得到合法解 # ============================ def sample_and_repair(sampler, Q, N, D): """ 一次取樣 + repair，即可保證得到合法 2-UAV M-TSP 解。 不需要反覆重試。 """ result = sampler.sample_qubo(Q, num_reads=30) sample = result.first.sample # 1) 先解出 slots u1_slots, u2_slots = decode_slots(sample, N) # 2) 依 slots 傾向分配城市給兩台 UAV assign1, assign2 = repair_routes_from_slots(u1_slots, u2_slots, N) # 3) 各自子集合內找最短路徑 u1_path, c1 = best_order_for_cities(assign1, D) u2_path, c2 = best_order_for_cities(assign2, D) total = c1 + c2 return u1_path, u2_path, c1, c2, total # ============================ # 9. Classic 2-UAV MTSP 暴力搜尋（全域最佳） # ============================ def classic_mtsp_two_uav_bruteforce(D): N = D.shape[0] cities = list(range(1, N)) best_total = float('inf') best_u1, best_u2 = None, None best_route = None def cost_of(path): return uav_cost(path, D) for perm in permutations(cities): for cut in range(len(perm)+1): u1 = list(perm[:cut]) u2 = list(perm[cut:]) total = cost_of(u1) + cost_of(u2) if total < best_total: best_total = total best_u1 = u1 best_u2 = u2 best_route = [0] + list(perm) return best_u1, best_u2, best_total, best_route # ============================ # 10. 共用：計算兩 UAV 總成本 # ============================ def compute_two_uav_cost(uav1_path, uav2_path, D): c1 = uav_cost(uav1_path, D) c2 = uav_cost(uav2_path, D) return c1 + c2, c1, c2 # ============================ # 11. SA & SQA：每 run 使用 sample_and_repair # ============================ def run_mtsp_sa_sqa(Q, N, D, NUM_RUNS=10): sa_costs = [] sa_routes = [] sa_u1_list = [] sa_u2_list = [] sa_uav_costs = [] # store tuple (c1, c2) sqa_costs = [] sqa_routes = [] sqa_u1_list = [] sqa_u2_list = [] sqa_uav_costs = [] # store tuple (c1, c2) sa = oj.SASampler() sqa = oj.SQASampler() print("\n🔥 Running SA (with repair, always feasible)...") for r in range(NUM_RUNS): u1, u2, c1, c2, total = sample_and_repair(sa, Q, N, D) full_route = [0] + u1 + u2 print(f"SA Run {r+1:02d}: UAV1={u1}, UAV2={u2}, " f"UAV1_cost={c1:.2f}, UAV2_cost={c2:.2f}, Total={total:.2f}") sa_costs.append(total) sa_routes.append(full_route) sa_u1_list.append(u1) sa_u2_list.append(u2) sa_uav_costs.append((c1, c2)) # <-- store both costs print("\n🔥 Running SQA (with repair, always feasible)...") for r in range(NUM_RUNS): u1, u2, c1, c2, total = sample_and_repair(sqa, Q, N, D) full_route = [0] + u1 + u2 print(f"SQA Run {r+1:02d}: UAV1={u1}, UAV2={u2}, " f"UAV1_cost={c1:.2f}, UAV2_cost={c2:.2f}, Total={total:.2f}") sqa_costs.append(total) sqa_routes.append(full_route) sqa_u1_list.append(u1) sqa_u2_list.append(u2) sqa_uav_costs.append((c1, c2)) # <-- store both costs sa_results = (sa_costs, sa_routes, sa_u1_list, sa_u2_list, sa_uav_costs) sqa_results = (sqa_costs, sqa_routes, sqa_u1_list, sqa_u2_list, sqa_uav_costs) return sa_results, sqa_results # ============================ # 12. 綜合分析圖表（你指定的版本） # ============================ def create_comprehensive_charts(sa_results, sqa_results, classic_results, D, N): """創建綜合分析圖表""" fig = plt.figure(figsize=(18, 12)) # 解包結果 sa_costs, sa_routes, sa_uav1, sa_uav2, sa_uav_costs = sa_results sqa_costs, sqa_routes, sqa_uav1, sqa_uav2, sqa_uav_costs = sqa_results classic_uav1, classic_uav2, classic_cost, classic_route = classic_results # --------------------------------------------------------- # 1. MTSP 成本分布比較 (左上) - 系統總成本 # --------------------------------------------------------- ax1 = plt.subplot(2, 3, 1) bins = range(int(min(sa_costs + sqa_costs)) - 1, int(max(sa_costs + sqa_costs)) + 2) ax1.hist(sa_costs, bins=bins, alpha=0.6, label="SA Total", density=True, color='lightblue') ax1.hist(sqa_costs, bins=bins, alpha=0.6, label="SQA Total", density=True, color='lightcoral') # 添加KDE if len(sa_costs) > 1: xs_sa, ys_sa = kde_1d(sa_costs) ax1.plot(xs_sa, ys_sa, label="SA KDE", color='blue', linewidth=2) if len(sqa_costs) > 1: xs_sqa, ys_sqa = kde_1d(sqa_costs) ax1.plot(xs_sqa, ys_sqa, label="SQA KDE", color='red', linewidth=2) ax1.axvline(x=classic_cost, color='green', linestyle='--', label=f'Classic: {classic_cost}', linewidth=2) ax1.set_title("Total System Cost Distribution") ax1.set_xlabel("Total Cost (UAV1 + UAV2)") ax1.set_ylabel("Density") ax1.legend() ax1.grid(True, alpha=0.3) # --------------------------------------------------------- # 2. 單一 UAV 成本分布比較 (右上) - 修正為「個別 UAV」視角 # --------------------------------------------------------- ax2 = plt.subplot(2, 3, 2) # 展平數據：將 [(c1, c2), (c1, c2)...] 變成 [c1, c2, c1, c2...] # 這樣可以看到「單台無人機」通常飛多遠 sa_single_costs = [c for costs in sa_uav_costs for c in costs] sqa_single_costs = [c for costs in sqa_uav_costs for c in costs] # 計算 classic 的單機成本 c1_classic = uav_cost(classic_uav1, D) c2_classic = uav_cost(classic_uav2, D) # 設定 bins all_single = sa_single_costs + sqa_single_costs uav_bins = range(int(min(all_single)) - 1, int(max(all_single)) + 2) ax2.hist(sa_single_costs, bins=uav_bins, alpha=0.6, label="SA Single UAV", density=True, color='skyblue') ax2.hist(sqa_single_costs, bins=uav_bins, alpha=0.6, label="SQA Single UAV", density=True, color='salmon') ax2.axvline(x=c1_classic, color='darkgreen', linestyle=':', label='Classic UAV1') ax2.axvline(x=c2_classic, color='limegreen', linestyle=':', label='Classic UAV2') ax2.set_title("Individual UAV Cost Distribution") ax2.set_xlabel("Cost per UAV") ax2.set_ylabel("Density") ax2.legend() ax2.grid(True, alpha=0.3) # --------------------------------------------------------- # 3. 箱型圖比較 (中上) - 修正重點 # --------------------------------------------------------- ax3 = plt.subplot(2, 3, 3) # 數據 1 & 2: 系統總成本 (Total Cost) # 數據 3 & 4: 單機成本 (Individual UAV Cost) - 使用上面展平的數據 # 這樣 Box Plot 會有明顯的高低落差（總成本高，單機成本低） box_data = [sa_costs, sqa_costs, sa_single_costs, sqa_single_costs] bp = ax3.boxplot( box_data, labels=["SA\nTotal", "SQA\nTotal", "SA\nSingle", "SQA\nSingle"], patch_artist=True, showmeans=True ) colors = ['lightblue', 'lightcoral', 'skyblue', 'salmon'] for patch, color in zip(bp['boxes'], colors): patch.set_facecolor(color) ax3.set_title("Cost Comparison: Total vs Single UAV") ax3.set_ylabel("Cost") ax3.grid(True, alpha=0.3) # --------------------------------------------------------- # 4. Route diversity heatmap - SA (左下) # --------------------------------------------------------- ax4 = plt.subplot(2, 3, 4) sa_mat = route_diversity_matrix(sa_routes, N) im1 = ax4.imshow(sa_mat, aspect='auto', origin='lower', cmap='viridis') ax4.set_title("SA Route Diversity") ax4.set_xlabel("Position") ax4.set_ylabel("City") plt.colorbar(im1, ax=ax4, shrink=0.8) # --------------------------------------------------------- # 5. Route diversity heatmap - SQA (右下) # --------------------------------------------------------- ax5 = plt.subplot(2, 3, 5) sqa_mat = route_diversity_matrix(sqa_routes, N) im2 = ax5.imshow(sqa_mat, aspect='auto', origin='lower', cmap='viridis') ax5.set_title("SQA Route Diversity") ax5.set_xlabel("Position") ax5.set_ylabel("City") plt.colorbar(im2, ax=ax5, shrink=0.8) # --------------------------------------------------------- # 6. 最佳路徑可視化 (中下) # --------------------------------------------------------- ax6 = plt.subplot(2, 3, 6) # 找出 SA 或 SQA 的最佳解 best_sa_idx = sa_costs.index(min(sa_costs)) best_sqa_idx = sqa_costs.index(min(sqa_costs)) best_sa_u1 = sa_uav1[best_sa_idx] best_sa_u2 = sa_uav2[best_sa_idx] best_sqa_u1 = sqa_uav1[best_sqa_idx] best_sqa_u2 = sqa_uav2[best_sqa_idx] # 用成本較好的那組 if min(sa_costs) <= min(sqa_costs): u1 = best_sa_u1 u2 = best_sa_u2 route_name = "SA" route_cost = min(sa_costs) else: u1 = best_sqa_u1 u2 = best_sqa_u2 route_name = "SQA" route_cost = min(sqa_costs) # --- 繪製城市 --- angles = np.linspace(0, 2*np.pi, N, endpoint=False) x_pos = np.cos(angles) y_pos = np.sin(angles) ax6.scatter(x_pos, y_pos, s=200, c='red', zorder=5) for i, (x, y) in enumerate(zip(x_pos, y_pos)): ax6.annotate(str(i), (x, y), ha='center', va='center', fontsize=10, fontweight='bold', color='white', zorder=6) # --- UAV1: 藍色 --- if len(u1) > 0: pts = [0] + u1 + [0] # 加入 depot xs = [x_pos[c] for c in pts] ys = [y_pos[c] for c in pts] ax6.plot(xs, ys, '-o', color='blue', linewidth=2, alpha=0.8, label=f'UAV1 ({len(u1)})') # --- UAV2: 橘色 --- if len(u2) > 0: pts = [0] + u2 + [0] # 加入 depot xs = [x_pos[c] for c in pts] ys = [y_pos[c] for c in pts] ax6.plot(xs, ys, '-o', color='orange', linewidth=2, alpha=0.8, label=f'UAV2 ({len(u2)})') ax6.set_title(f"Best {route_name} MTSP Solution\nTotal Cost: {route_cost:.2f}") ax6.set_xlim(-1.3, 1.3) ax6.set_ylim(-1.3, 1.3) ax6.set_aspect('equal') ax6.axis('off') ax6.legend(loc='upper right') plt.tight_layout() plt.savefig("mtsp_two_uav_comprehensive_analysis.png", dpi=300, bbox_inches='tight') print(f"\n📊 綜合分析圖表已保存: mtsp_two_uav_comprehensive_analysis.png") plt.show() # ============================ # 13. main：整合執行 # ============================ if __name__ == "__main__": # 距離矩陣：10 城市 D = np.array([ [0, 2, 8, 5, 7, 6, 3, 9, 4, 2], [2, 0, 5, 7, 3, 8, 4, 6, 9, 1], [8, 5, 0, 2, 6, 7, 3, 4, 1, 5], [5, 7, 2, 0, 4, 3, 8, 6, 2, 7], [7, 3, 6, 4, 0, 5, 9, 2, 7, 3], [6, 8, 7, 3, 5, 0, 4, 7, 9, 6], [3, 4, 3, 8, 9, 4, 0, 5, 6, 2], [9, 6, 4, 6, 2, 7, 5, 0, 8, 3], [4, 9, 1, 2, 7, 9, 6, 8, 0, 5], [2, 1, 5, 7, 3, 6, 2, 3, 5, 0] ]) N = D.shape[0] print("🚀 2-UAV M-TSP (Quantum + Repair vs Classic) 開始運行...\n") print(f"Distance Matrix ({N}x{N}):") print(D) # 建立 QUBO Q, _ = build_mtsp_qubo_variable(D, penalty=20.0) # SA / SQA，每 run 一定是合法解 NUM_RUNS = 10 sa_results, sqa_results = run_mtsp_sa_sqa(Q, N, D, NUM_RUNS=NUM_RUNS) # Classic 暴力全域最佳 print("\n🎯 Running Classic 2-UAV MTSP (Bruteforce ALL solutions)...") classic_uav1, classic_uav2, classic_total_cost, classic_route = classic_mtsp_two_uav_bruteforce(D) print(f"Classic UAV1={classic_uav1}, UAV2={classic_uav2}, Cost={classic_total_cost}") print(f"Classic merged route (0 + perm): {classic_route}") # Summary sa_costs, _, _, _, _ = sa_results sqa_costs, _, _, _, _ = sqa_results print("\n📊 Result Summary:") print(f"SA best cost = {min(sa_costs):.2f}, mean = {np.mean(sa_costs):.2f}") print(f"SQA best cost = {min(sqa_costs):.2f}, mean = {np.mean(sqa_costs):.2f}") print(f"Classic global optimum = {classic_total_cost:.2f}") # 畫圖 classic_results = (classic_uav1, classic_uav2, classic_total_cost, classic_route) print("\n🎨 Creating comprehensive analysis charts...") create_comprehensive_charts(sa_results, sqa_results, classic_results, D, N) print("\n🏁 Done.")